Appendix IIThe
Effect of Carbon Dioxide on pH

Carbon dioxide (CO2) is an acid anhydride, which means that
when it is dissolved in water it lowers the pH of the solution. In fact
pure rainwater has a pH of 5.6 because of the 360 ppm atmospheric
concentration of CO2. During World War II, atmospheric
concentrations of CO2 were closer to 330 ppm, but that is not
an important difference for the purposes addressed here. One
can think of the process as having three steps all of which involve a
chemical equilibrium. The first step is the dissolution of
CO2 in water; its equilibrium constant is the Henry's
Law constant of CO2, Khc:

CO2 + H2O <=> H2CO3

The second step is the acid base reaction between carbonic acid and
water; its equilibrium constant is denoted here as Kc1:

H2CO3 + H2O <=>
H3O+ + HCO3-

The third step is reaction between the bicarbonate ion
(HCO3-) and water whose equilibrium constant is here
denoted as Kc2:

HCO3- + H2O <=>
H3O+ + CO32-

Also, one needs to consider the autoprotolysis of water:

2H2O <=> H3O+ + OH-

In aqueous solution, one can treat the concentration of water as a
constant and derive a constant for the equilibrium, Kw.
These constants and their associated enthalpies are reported in
Seinfeld. 1
Here is a table of the relevant quantities:

The slight temperature dependence of these constants can be accounted
for by means of the enthalpies given. The pH of a solution is defined
as -log[H+] where [H+] is the concentration of
hyronium ions in moles/liter. From the information given it is possible
to derive a cubic equation expressing the relationship between
[H+] and the partial pressure of CO2,
PCO2. This equation is also presented in
Seinfeld: 1

[H+]3 - (Kw+KhcKc1
PCO2)[H+]-2+KhcKc1
Kc2PCO2=0

I solved this equation by means of a simple computer program employing a
rootfinding method similar to Newton's method.
2
The results are shown in figure II.1.